One-to-one correspondence between thermal structure factors and coupling constants of general bilinear Hamiltonians

Abstract

A theorem that establishes a one-to-one relation between zero-temperature static spin-spin correlators and coupling constants for a general class of quantum spin Hamiltonians bilinear in the spin operators has been recently established by J. Quintanilla, using an argument in the spirit of the Hohenberg-Kohn theorem in density functional theory. Quintanilla's theorem gives a firm theoretical foundation to quantum spin Hamiltonian learning using spin structure factors as input data. Here we extend the validity of the theorem in two directions. First, following the same approach as Mermin, the proof is extended to the case of finite-temperature spin structure factors, thus ensuring that the application of this theorem to experimental data is sound. Second, we note that this theorem applies to all types of Hamiltonians expressed as sums of bilinear operators, so that it can also relate the density-density correlators to the Coulomb matrix elements for interacting electrons in the lowest Landau level.

arXiv comment4 pages

References in corpus (15)

• Quantum Computing in the NISQ era and beyond
• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Noisy intermediate-scale quantum (NISQ) algorithms
• Models and Materials for Generalized Kitaev Magnetism
• Observation of fractional edge excitations in nanographene spin chains
• Experimental Quantum Hamiltonian Learning
• Hamiltonian Learning and Certification Using Quantum Resources
• Sample-efficient learning of quantum many-body systems
• Nonuniqueness of the Potentials of Spin-Density-Functional Theory
• Extracting density-density correlations from in situ images of atomic quantum gases
• Scalable Hamiltonian learning for large-scale out-of-equilibrium quantum dynamics
• Spin-distribution functionals and correlation energy of the Heisenberg model
• Learning Effective Spin Hamiltonian of Quantum Magnet